Formalizing Elements of Probabilistic Mechanics

TL;DR

This paper develops a probabilistic model of particle motion on a 3D lattice using discrete random walks, deriving analogues of classical Newtonian laws and suggesting applications to thermodynamics.

Contribution

It introduces a rigorous probabilistic framework for particle dynamics that parallels classical mechanics and can extend to thermodynamic law justification.

Findings

Derived probabilistic analogues of Newton's laws

Constructed a rigorous probability space for particle trajectories

Potentially applicable to thermodynamics laws

Abstract

In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in classical mechanics, here we use probabilistic properties of particle movement to formally derive analogues of Newton's first and second laws of motion. Similar probabilistic models can potentially be applied to justify laws of thermodynamics in a consistent manner.